Abstract
We present a study of the interaction between Josephson junctions in circular superconducting rings and non-classical microwaves, treating both quantum mechanically. A Hamiltonian that describes both inductive and capacitive coupling between the two systems is derived within the external field approximation. Other Hamiltonians which go beyond the external field approximation, and describe explicitly the interaction of the quantum circuit that produces the non-classical microwaves with the Josephson junction circuit, are also presented. A comparison between current experiments which use classical electromagnetic fields and the proposed experiments that use non-classical microwaves, is made.
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